Influence diagnostics in semiparametric regression models

In this paper we consider the semiparametric regression model, Y=x'[beta]+m(t)+[var epsilon], and provide some influence diagnostics for estimators of [beta], m and the mean response x'[beta]+m(t). We express these influence diagnostics as functions of the residuals and leverages. We find that an influential observation on the estimator of the coefficient vector [beta] may not be influential on that of the nonparametric component m, and vice versa. Also, an observation which is not influential on each of them may be influential on the estimator of the mean response. Therefore, influence of an observation should be evaluated on each estimator separately. An illustrative example based on a real data set is also given.